Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2143
... extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF . For ...
... extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF . For ...
Page 2530
... extensions of J - symmetric operators with adjoint . Comm . Pure Appl . Math ... selfadjoint differential operators . Doklady Akad . Nauk SSSR 158 , 29–32 ( 1964 ) ... adjoint operators . Expansion in generalized eigenelements . Ann . Inst ...
... extensions of J - symmetric operators with adjoint . Comm . Pure Appl . Math ... selfadjoint differential operators . Doklady Akad . Nauk SSSR 158 , 29–32 ( 1964 ) ... adjoint operators . Expansion in generalized eigenelements . Ann . Inst ...
Page 2551
... adjoint extensions of a symmetric operator . Pacific J. Math . 12 , 1003-1022 ( 1962 ) . 2. Spectral measures ... Expansion in eigenfunctions of a non - self - adjoint singular differential operator of second order . Mat . Sbornik N. S. ...
... adjoint extensions of a symmetric operator . Pacific J. Math . 12 , 1003-1022 ( 1962 ) . 2. Spectral measures ... Expansion in eigenfunctions of a non - self - adjoint singular differential operator of second order . Mat . Sbornik N. S. ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero